Quantitative measurement of bone mineral in excised bone from roentgenograms using FIDAC and a computer.

Abstract

The quantitative determination of absolute bone mass has been used for the characterization of normal and diseased bone structures. This report describes a technic, currently in the development stage, for very fast, large-scale research studies of bone densitometry. The method employs the flying-spot densitometer FIDAC (Film Input to Digital Automatic Computer) to scan the x-ray film on which the excised bone and standard aluminum step wedge have been imaged. The digital representation of the optical density of the entire film is stored in the memory of an IBM 360/44 computer for automatic processing by the appropriate programs. The FIDAC is capable of scanning up to 4,000,000 points per film frame within four seconds, each point being interpreted as one of sixteen gray density levels. The scanning spot size is 40 μ in diameter. The basis for the calculation of bone mineral concentration involves the law of attenuation: where I is the intensity of the x ray transmitted through the specimen and recorded on the film. I0 is the intensity of the x rays incident on the specimen. μ is the linear attenuation coefficient in cm−1. and τ is the thickness of the specimen in cm. Because the linear absorption coefficient, μ; is wave-length-dependent, a tantalum foil filter was placed at the exit window of the x-ray tube to yield essentially monochromatic Kα tungsten radiation. The silver deposition on the film is directly related to the radiation energy absorbed by the film at that spot. The gray levels measured by the FIDAC are inversely proportional to the silver deposition. The product of mass attenuation coefficient (μ/p)Al anddensity (dAl) may be substituted in place of linearattenuation coefficient, hence: where V0 is the FIDAC voltage corresponding to the gray level for the incident radiation. V is the voltage corresponding to the gray level obtained with the aluminum step wedge for the respective thickness, τAl. V0 and dAl are calculated from any two aluminum step-wedge thicknesses and their related FIDAC gray level values, V, so that the entire range of gray level values measured by FIDAC may be determined in terms of equivalent aluminum wedge. For equivalent gray levels from aluminum wedge and from bone: where db is the density of the bone and (μ/p)b is the mass attenuation coefficient for bone assumed to be calcium hydroxyapatite. The density of aluminum is given by: where wtAl is the weight of aluminum.Δx Δy is the area of aluminum covered by a FIDAC spot. Since the thickness and corresponding density of aluminum step wedge used and the area of the FIDAC scanning light spot are known, the equivalent weight of aluminum gray level under each FIDAC spot can be calculated. From this, the weight of bone having the same gray level can be determined from: The weight of bone thus calculated from each gray level spot can be summed for all spots to give the total weight of bone mineral in the specimen used. This total weight can then be related to the bone volume which is measured in the experiment by other means.